Problem: Solve for $x$ and $y$ using substitution. ${-2x+6y = -10}$ ${y = x-7}$
Explanation: Since $y$ has already been solved for, substitute $x-7$ for $y$ in the first equation. ${-2x + 6}{(x-7)}{= -10}$ Simplify and solve for $x$ $-2x+6x - 42 = -10$ $4x-42 = -10$ $4x-42{+42} = -10{+42}$ $4x = 32$ $\dfrac{4x}{{4}} = \dfrac{32}{{4}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {y = x-7}\thinspace$ to find $y$ ${y = }{(8)}{ - 7}$ $y = 1$ You can also plug ${x = 8}$ into $\thinspace {-2x+6y = -10}\thinspace$ and get the same answer for $y$ : ${-2}{(8)}{ + 6y = -10}$ ${y = 1}$